Given : A rhombus ABCD whose diagonals intersect each other at O.
To prove : A circle with AB as diameter passes through O.
Proof : ∠AOB = 90°
[Diagonals of a rhombus bisect each other at 90°]
⇒ ∆AOB is a right triangle right angled at O.
⇒ AB is the hypotenuse of A B right ∆AOB.
⇒ If we draw a circle with AB as diameter, then it
will pass through O. because angle is a semicircle is 90° and ∠AOB = 90° Proved.